I am free to make my own definitions when making a point. Is my definition not grammatically correct? Does it not connect a subject and a predicate? I have used SK's process. You must deal with my definition. It is consistent with the proposed philosophy in question.

My point is that often when we form a concept we do not know how many subjects are subsumed by that concept. When the concept of complete ordered field was created, it was unclear that there were any. Then two distinct constructions were made: Dedekind cuts and equivalence classes of Cauchy Sequences. It was not clear that these weren't distinct initially. It appeared that there were two subjects in this concept until it was proved that these two are isomorphic representations of the same thing. Finally, it was proved that all complete ordered fields are isomorphic to the so-called real numbers. Was "complete ordered field" never a concept, even when it appeared that there were two distinct constructions? Did this label not function in every respect as a concept despite the fact that there exists only one? While "real numbers" is the name of a subject, isn't "complete ordered field" still a concept for which there is only one applicable subject, the real numbers? This, I believe, is a fair point to make in discussing what we mean by "concept".
I have another point to make. Consider the following definition:
Definition: A dragon is a flying reptile that breathes fire.
Everyone knows that a flying reptile that breathes fire is a dragon. However, this concept is invalid because there are no subjects/units to which it applies. We do not have two or more units isolated by these characteristics. We don't even have one! However, it is hard to say that dragons are not concepts. They just happen to be invalid concepts.

SK,
First off, thank you for kicking off an interesting discussion. It has been most enjoyable.
Now, I don't understand what you say on page 6 paragraph 3. In particular, you say
I do not know what "subly" is. Was this supposed to be "subtly"?
Let me subtly assume the existence of a concept that is tailor-made, etc. There is a concept in mathematics called a field. Examples of fields include the real numbers, complex numbers, finite fields and so on. Would it be fair to say that the concept "field" subsumes these subjects? Now, there is something called a complete field. Examples of complete fields include real numbers and complex numbers, etc. These subjects are subsumed by the concept "complete field". Finally, there is something called a complete ordered field. It seems to me that this is a concept. I have combined well-defined concepts to form a new concept. A priori, one does not know whether there exist any such subjects until once shows that the real numbers do in fact constitute a complete ordered field. Therefore we know that this is not an empty notion. Also, a priori one does not know how many such subjects exist. However, there is a proof that, up to isomorphism, there is only one such subject, the real numbers.
Was "complete ordered field" never a concept? If it was a concept until it was shown that there was only one, at what point did it cease to be a concept? Was it no longer a concept when someone first proved that there was only one such subject? What is a concept in your own mind until someone informed you of the proof that there was only one, making "authority" the determining factor concerning concepts. Or, was it once you read and understood the proof that it ceased to be a concept?
I believe that "complete ordered field" is a concept despite the fact that there is only one. Was this a cheap shot?

This whole thread seems like quibbling over minutiae--about issues that cannot in any way affect me. Cruz supports getting the government out of our business and keeping to a limited view of government's role in our lives. Compare that to Hillary Clinton, a statist, who believes in the intrinsic right of government to interfere in every aspect of your life. What about Trump, a narcissist, who is governed by whim? You can expect him to do random acts of horrible governance.
The point is, you can look at each of the candidates and conclude that their ideas are at variance with your own. What really matters is, who is most likely to "Get the Hell out of my way!"? I believe that Cruz is the only candidate that qualifies. Even with respect to abortion, he is most likely to say that it is a matter for the States and not for the Federal Government. Corrupticrat Clinton, Whim worshipping Trump, or principled Cruz--I take Cruz.

CoryDeskins, Your professor's ire at your comments indicates that she cannot be reasoned with. Don't try to reason someone out of a position that they did not reason themselves into. She felt her way into her opinions and there is nothing you can do about that.
Concerning your intellectual isolation, I can relate. It is almost as though you are a different species. From the conceptual point of view, you are and that's a good thing. Perhaps someday cultures will evolve from their current pitiful conditions. That said, there is nothing in this world that can prevent you from achieving good things. Let the Law of Causality be your guide.

This is entirely a question of values, not of facts. One who is innured to an act will not have much emotional response to it. Similarly, one can suppress an emotional response through rationalization. Emotional responses are based upon ones values.
When the umbilical cord is cut, a fetus becomes a baby and achieves the virtue of independence. Absurd! The new baby is certainly not more rational after cutting the umbilical. It doesn't gain life when cutting the umbilical. If your claim is that it becomes "human" at that point, you are experiencing an extreme case of rationalization designed for a purpose. Applying labels, such as "fetus", is a similar rationalization.
The real question is not whether the object in question is living or human but whether it has value. People are known to define classes of humans as having no value so that they can exterminate them. They deny their humanity for this purpose. They give them labels for this purpose. Medical experiments on those having their humanity denied is not unheard of.
Just because Ayn Rand became sterile through a botched abortion does not justify abortion. One can understand her rationalizations on the subject, expecially given the times in which she lived. People were told that "fetuses" were just so much tissue. This too is just a rationalization designed to label and deny the humanity of the object in question.
That Planned Parenthood is selling baby body parts is a logical extension of the rationalizations that go into the corporation's very existence.
The unborn has value as an end in itself. It has value in the same way other human beings have value. That is the underlying reason why these videos are sickening. We should have evolved beyond this by now. We remain a primitive an unevolved species still capable of rationalizing horrible crimes. These "fetuses" struggle and squirm to escape the instruments that crush them. That struggle to survive is an expression of value much deeper than rationalizations about independence.

That these babies have value is obvious (since they are being sold for parts). Using words like "fetus" is only misdirection from the fact that these are human, living, and feel pain when they are killed. One of you once said that since you consider these only as tissue that you would go to Planned Parenthood and have a BBQ eating the "tissue". I guess that would make you Cap' N Crunch.
At the very least, can we agree that no government monies should go to Planned Parenthood, just as no corporation of any kind should receive subsidies? Can we agree to that?
(We should also be able to agree that the sale of fetal lungs, livers, brains, leg muscles and the like is a violation of current federal law and those engaged in it should be sent to federal penitentiaries. We should also agree that what is seen in the recent videos is abhorrent.)

Watching the gargoyles haggling over prices for baby body parts in videos such as that found here (https://youtu.be/jjxwVuozMnU ) is sickening. Surely we can agree that profiteering off of lungs, livers, brains and leg muscles is morally wrong. The game of selling service contracts is a ruse to conceal these sales and avoid felony convictions concerning existing laws against such sales. That deception is also morally wrong. The only question that remains is, "Do you want your babies crunchy or not?"

Collectivist,
Hasn't the collectivist nature of people in the United States been worse before? Wasn't it worse in the 1930's? A significant number of people in the US supported Mussolini and many others supported Stalin. As pointed out above, Bill Clinton was responsible for letting North Korea get nukes. Harry Truman's devotion to the United Nations prevented any sort of "victory" in Korea and Eisenhower went along. Same goes for LBJ in Vietnam. It seems to me that the lesson here is that negotiations and entanglements together with international partners precludes attainment of national interests. This can be seen in Bush 41's failure to fully accomplish national goals in the first gulf war, deferring the inspection of WMD sites till later and to UN inspectors. The failure to finish the job was due to the squeemishness of "coalition partners". Seventeen UN resolutions later Bush 43 invaded Iraq together with a "coalition".
I am hopeful that secure communications will enable free peoples to associate at a level beyond governmental interference. These "super" men will compel governments to limit their roles to a more appropriate and tolerable level. The new Silk Road may have been a first glimmer of an evolution beyond the nation state. My "faith" may be misplaced.
This agreement (not a treaty) with Iran is yet another example of human failure to learn the lessons of history. Obama may think that he is charting a new course but in reality it is the same ol' same ol'.

By releasing the $100 Billion that has been frozen, we are in effect paying for their entire nuclear program. They get nukes whenever they want and europeans get a lot of lucrative arms deals. Is the world safer because of this?

It is my observation that Catholic societies are more left-leaning while protestant societies are more right-leaning. I believe that this stems from the Spanish colonial centralized form of government and legal system in the former. The British common law legal system is predominant in the latter, except in India which became independent in the golden age of socialism.

Indeed. On her death-bed you cannot possibly be trying to persuade her of anything. If you can comfort her in the manner she requests, then you are showing her human compassion and respect. Isn't this objectively the right thing to do? Besides, you are not practicing religion for your own sake by reading religious passages to a dying woman. You are enabling your grandmother to practice her own faith. Well done.

It must be pointed out that the industrial revolution was underway at least a century before you claim and its effects were commented on by observers such as Adam Smith in 1776. What is more, we have the example of the agrarian south vs the industrial north and who won that conflict. There are monuments to industry all over the place, including sky scrapers, sports arenas, rail road stations that resemble cathedrals, etc. These are not just syllogisms or worse, simple inferrences from analogies.
It is true that there are monuments to the industrial capacity of communists, but there are two great motives: Fear of risk and promise of reward. Stalin could motivate workers through fear. The alternative is preferable, in my view and we have the history of bare soviet shelves as evidence as to which system works better. Western nations muddy the philosophical waters by having "mixed" systems.
But I am getting too far afield of your original point. I contest the premise of your original post. Even so, there is considerable historical evidence that free enterprise works and is preferable to historical alternatives.